Find the integral of dx/sqrt(2-5x)
and the integral of dx/(x+3)
and the integral of dx/(x+3)
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the 1st is equal to integral of (2-5x)^-1/2
u=2-5x
du=-5 dx
du/-5=dx
-1/5 integral u^-1/2
-1/5 *(1/1+(-1/2)) u^1/2
-1/5*(1/(1/2)u^1/2
-1/5*2*u^1/2
(-2/5)u^1/2
(-2/5)(2-5x)^1/2
-2/5 *sqrt(2-5x)
the 2nd is
dx/(x+3)
u=x+3
du=dx
du/u
ln u
ln(x+3)
u=2-5x
du=-5 dx
du/-5=dx
-1/5 integral u^-1/2
-1/5 *(1/1+(-1/2)) u^1/2
-1/5*(1/(1/2)u^1/2
-1/5*2*u^1/2
(-2/5)u^1/2
(-2/5)(2-5x)^1/2
-2/5 *sqrt(2-5x)
the 2nd is
dx/(x+3)
u=x+3
du=dx
du/u
ln u
ln(x+3)
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1) use substitution u = 2 - 5x
2) u = x + 3
2) u = x + 3